Gallatin is a wonderful opportunity that you should seriously consider. Think of Gallatin as doing a double or triple major, but you’re taking the essence of each discipline and mixing them together to form a concentration/course of study.
You can pretty much find people studying anything at Gallatin. You can definitely work Game Design into your concentration (see: http://gallatin.nyu.edu/studentlife/profiles/alumni-grad/michael-t-astolfi.html)
The only difference is that you’ll have to incorporate other influences into your concentration, say Computer Science, or Digital Media, or Neuroscience.